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The reference value for ρ b for b = 0 is the defined sea level value, ρ 0 = 1.2250 kg/m 3 or 0.0023768908 slug/ft 3. Values of ρ b of b = 1 through b = 6 are obtained from the application of the appropriate member of the pair equations 1 and 2 for the case when h = h b+1. [2] In these equations, g 0, M and R * are each single-valued ...
The Taylor polynomials for ln(1 + x) only provide accurate approximations in the range −1 < x ≤ 1. For x > 1, Taylor polynomials of higher degree provide worse approximations. The Taylor approximations for ln(1 + x) (black). For x > 1, the approximations diverge. Pictured is an accurate approximation of sin x around the point x = 0. The ...
ρ (Greek letter rho) is the fluid mass density (e.g. in kg/m 3), and; u is the flow speed in m/s. It can be thought of as the fluid's kinetic energy per unit volume. For incompressible flow, the dynamic pressure of a fluid is the difference between its total pressure and static pressure. From Bernoulli's law, dynamic pressure is given by
Visualization of an unstable Rayleigh–Taylor instability configuration where baroclinic torque at the interface creates vorticity and induces a velocity field that increases the baroclinic torque. Here ω is vorticity, p is pressure, ρ is density, u is velocity and g is gravity. The thick circular arrows represent the velocity field created ...
, is the gas film specific heat at constant pressure (J.Kg −1.K −1) The droplet vaporization rate can be expressed as a function of the Sherwood number. The Sherwood number describes the non-dimensional mass transfer rate to the droplet and is defined as: [3]
Itô's lemma can be used to derive the Black–Scholes equation for an option. [2] Suppose a stock price follows a geometric Brownian motion given by the stochastic differential equation dS = S(σdB + μ dt). Then, if the value of an option at time t is f(t, S t), Itô's lemma gives
Taylor dispersion or Taylor diffusion is an apparent or effective diffusion of some scalar field arising on the large scale due to the presence of a strong, confined, zero-mean shear flow on the small scale. Essentially, the shear acts to smear out the concentration distribution in the direction of the flow, enhancing the rate at which it ...
Using ideal gas equation of state for constant temperature process (i.e., / is constant) and the conservation of mass flow rate (i.e., ˙ = is constant), the relation Qp = Q 1 p 1 = Q 2 p 2 can be obtained. Over a short section of the pipe, the gas flowing through the pipe can be assumed to be incompressible so that Poiseuille law can be used ...